Non-linear spatial Timoshenko beam element with curvature interpolation

Abstract

The paper presents a spatial Timoshenko beam element with a total Lagrangian formulation. The element is based on curvature interpolation that is independent of the rigid-body motion of the beam element and simplifies the formulation. The section response is derived from plane section kinematics. A two-node beam element with constant curvature is relatively simple to formulate and exhibits excellent numerical convergence. The formulation is extended to N-node elements with polynomial curvature interpolation. Models with moderate discretization yield results of sufficient accuracy with a small number of iterations at each load step. Generalized second-order stress resultants are identified and the section response takes into account non-linear material behaviour. Green–Lagrange strains are expressed in terms of section curvature and shear distortion, whose first and second variations are functions of node displacements and rotations. A symmetric tangent stiffness matrix is derived by consistent linearization and an iterative acceleration method is used to improve numerical convergence for hyperelastic materials. The comparison of analytical results with numerical simulations in the literature demonstrates the consistency, accuracy and superior numerical performance of the proposed element. Copyright © 2001 John Wiley & Sons, Ltd.